NegCycleFinderQ class

Negative Cycle Finder with constraints using Howard's method.

Template parameters
DiGraph	Type of the directed graph representation
Domain	Numeric type for distance calculations

This class extends the basic negative cycle detection to support constrained optimization problems. It implements both predecessor and successor versions of Howard's algorithm, providing flexibility in how cycles are detected and how distance updates are constrained.

Algorithm variants:

Predecessor-based (howard_pred):
- Follows traditional Bellman-Ford relaxation
- Updates dist[v] based on dist[u] + weight(u,v)
- Useful when constraints apply to forward updates
```
Predecessor relaxation: dist[v] > dist[u] + w(u,v)
a -----> b becomes: pred[b] = a
```
Successor-based (howard_succ):
- Uses reverse relaxation logic
- Updates dist[u] based on dist[v] - weight(u,v)
- Useful when constraints apply to backward updates
```
Successor relaxation: dist[u] < dist[v] - w(u,v)
a -----> b becomes: succ[a] = b
```

Constraint handling:

The UpdateOk callback controls when distance updates are allowed
This enables domain-specific constraints and optimization strategies
Can implement bounds, step size limits, or custom validation

Template requirements:

DiGraph: Same as basic NegCycleFinder
Domain: Numeric type for distance calculations

Constructors, destructors, conversion operators

NegCycleFinderQ(const DiGraph& digraph) explicit: Initialize the negative cycle finder with a directed graph.

Public functions

template<typename Mapping, typename GetWeight, typename UpdateOk> auto howard_pred(Mapping& dist, GetWeight&& get_weight, UpdateOk&& update_ok) -> cppcoro::generator< Cycle > -> auto: Find negative cycles using predecessor-based Howard's algorithm.
template<typename Mapping, typename GetWeight, typename UpdateOk> auto howard_succ(Mapping& dist, GetWeight&& get_weight, UpdateOk&& update_ok) -> cppcoro::generator< Cycle > -> auto: Find negative cycles using successor-based Howard's algorithm.

Function documentation

template<typename DiGraph, typename Domain>
NegCycleFinderQ<DiGraph, Domain>::NegCycleFinderQ(const DiGraph& digraph) explicit

Initialize the negative cycle finder with a directed graph.

Parameters
digraph	A directed graph represented as a nested mapping

template<typename DiGraph, typename Domain> template<typename Mapping, typename GetWeight, typename UpdateOk>
auto NegCycleFinderQ<DiGraph, Domain>::howard_pred(Mapping& dist, GetWeight&& get_weight, UpdateOk&& update_ok) -> cppcoro::generator< Cycle >

Find negative cycles using predecessor-based Howard's algorithm.

Template parameters
Mapping	Distance mapping type
GetWeight	Callable type for getting edge weights
UpdateOk	Callable type for update constraint
Parameters
dist	Initial distance estimates (often zero-initialized)
get_weight	Function to get weight of an edge
update_ok	Function to determine if distance updates are allowed
Returns	cppcoro::generator<Cycle> Each negative cycle found as a list of edges

template<typename DiGraph, typename Domain> template<typename Mapping, typename GetWeight, typename UpdateOk>
auto NegCycleFinderQ<DiGraph, Domain>::howard_succ(Mapping& dist, GetWeight&& get_weight, UpdateOk&& update_ok) -> cppcoro::generator< Cycle >

Find negative cycles using successor-based Howard's algorithm.

Template parameters
Mapping	Distance mapping type
GetWeight	Callable type for getting edge weights
UpdateOk	Callable type for update constraint
Parameters
dist	Initial distance estimates (often zero-initialized)
get_weight	Function to get weight of an edge
update_ok	Function to determine if distance updates are allowed
Returns	cppcoro::generator<Cycle> Each negative cycle found as a list of edges

#include <digraphx/neg_cycle_q.hpp> template<typename DiGraph, typename Domain> NegCycleFinderQ class